I do belive the trend in the Catholic church is toward the Republican party but the marriage between the Catholic church and Democrat party is difficult to change. By no means do I mean all Catholics are Democrats. I mean that those who are still there are probably still there because of the Democrat tradition.
I suspect there are a lot of independants. I know there's a lot in the Orthodox churches as neither party seems real Christian to folks who immigrate here from Serbia (for instance) and find both are all for giving Muslims control of the former religious center of Serbia.
Personally I think at least supporting the Republicans keeps the abject marxists from taking over, but for some it's too much of a bitter choice.